10 important short questions from each of the 14 chapters of Class 11 Math (2025 Syllabus)

 Here are 10 important short questions from each of the 14 chapters of Class 11 Math (2025 Syllabus):

Chapter 1: Sets

  1. What is a set?

  2. Define null and singleton set.

  3. What is a power set?

  4. Difference between subset and proper subset.

  5. Define universal set.

  6. What is the union of two sets?

  7. What is the intersection of two sets?

  8. Draw Venn diagram for A ∪ B.

  9. What is the complement of a set?

  10. If A = {1, 2}, B = {2, 3}, find A ∪ B.

Chapter 2: Relations and Functions

  1. Define relation with example.

  2. What is a function?

  3. Define domain, co-domain, and range.

  4. What is one-one function?

  5. What is onto function?

  6. Define identity function.

  7. Define inverse of a function.

  8. What is constant function?

  9. If f(x) = x + 2, find f(3).

  10. Graph of linear function looks like?

Chapter 3: Trigonometric Functions

  1. Define all 6 trigonometric ratios.

  2. Convert 60° to radian.

  3. Convert π/3 to degree.

  4. What is unit circle?

  5. Evaluate sin 45°, tan 30°.

  6. What is periodic function?

  7. Prove sin²x + cos²x = 1.

  8. Domain of cot x?

  9. Solve sin x = 1/2.

  10. Find principal value of tan⁻¹1.

Chapter 4: Principle of Mathematical Induction

  1. What is mathematical induction?

  2. Write the steps of induction method.

  3. Prove 1 + 2 + 3 + ... + n = n(n+1)/2.

  4. What is base case in induction?

  5. State the principle of mathematical induction.

  6. Prove 2ⁿ > n² for n ≥ 5.

  7. What is inductive hypothesis?

  8. Prove 3ⁿ - 1 is divisible by 2.

  9. Is induction valid for all numbers?

  10. Use induction to prove: 1² + 2² + ... + n².

Chapter 5: Complex Numbers and Quadratic Equations

  1. What is a complex number?

  2. Define imaginary unit i.

  3. Write the standard form of complex number.

  4. What is the conjugate of a complex number?

  5. What is the modulus of a complex number?

  6. Simplify (2 + 3i) + (1 - 2i).

  7. Multiply (1 + i)(1 - i).

  8. Solve x² + 1 = 0 over complex numbers.

  9. What is discriminant in a quadratic equation?

  10. Define roots of a quadratic equation.

Chapter 6: Linear Inequalities

  1. What is a linear inequality?

  2. Difference between equation and inequality.

  3. Graph x > 3.

  4. Solve 2x - 5 < 7.

  5. What is solution set of inequality?

  6. Solve the inequality: 3x + 4 ≤ 10.

  7. What is intersection of inequalities?

  8. Represent solution of x + 2 > 0 on number line.

  9. Define compound inequality.

  10. Graphical solution of x + y ≤ 5, x, y ≥ 0.


Chapter 7: Permutations and Combinations

  1. Define permutation.

  2. Define combination.

  3. Difference between permutation and combination.

  4. Find the number of permutations of 5 different books.

  5. What is nPr?

  6. What is nCr?

  7. Find 5C2.

  8. In how many ways can 3 out of 5 students be selected?

  9. If nP2 = 56, find n.

  10. How many 3-digit numbers can be formed using 1, 2, 3, 4?

Chapter 8: Binomial Theorem

  1. State the binomial theorem.

  2. Expand (a + b)².

  3. What is the general term of binomial expansion?

  4. What is the middle term in the expansion of (x + y)⁶?

  5. Find the 4th term in (1 + x)⁵.

  6. Expand (x - 2)³.

  7. Define binomial coefficient.

  8. Value of ⁵C₂?

  9. Find coefficient of x² in (1 + x)⁴.

  10. How many terms are in the expansion of (a + b)ⁿ?

Chapter 9: Sequences and Series

  1. Define arithmetic progression (A.P.).

  2. Define geometric progression (G.P.).

  3. Find the nth term of an A.P.

  4. What is the sum of first n terms of an A.P.?

  5. If a = 2, d = 3, find 5th term.

  6. Define harmonic progression.

  7. What is the common ratio in G.P.?

  8. Find the sum of first 3 terms of 2, 4, 8,...

  9. Relation between A.M. and G.M.?

  10. If a, b, c are in G.P., show that b² = ac.

Chapter 10: Straight Lines

  1. Define slope of a line.

  2. What is the slope-intercept form of a line?

  3. Equation of line passing through (0, 4) and slope 2?

  4. What is point-slope form?

  5. Find slope of line joining (1,2) and (3,6).

  6. What is intercept of a line?

  7. Define collinear points.

  8. Write general equation of straight line.

  9. If slope m = 0, what is the line like?

  10. Find distance between two parallel lines.

Chapter 11: Conic Sections

  1. Define conic section.

  2. What is a parabola?

  3. Write standard form of ellipse.

  4. Define eccentricity.

  5. Equation of circle with center (0,0) and radius r?

  6. What is the focus of parabola?

  7. Define directrix.

  8. What is latus rectum?

  9. Equation of hyperbola?

  10. Difference between ellipse and hyperbola?

Chapter 12: Introduction to Three Dimensional Geometry

  1. Define 3D geometry.

  2. Coordinates of a point in 3D?

  3. What is the distance formula in 3D?

  4. Midpoint formula in 3D?

  5. Find distance between (1,2,3) and (4,5,6).

  6. What is section formula in 3D?

  7. Define coordinate axes.

  8. What are octants?

  9. Define origin in 3D space.

  10. What is the x-y plane?

Chapter 13: Limits and Derivatives

  1. Define limit.

  2. What is derivative?

  3. Find lim(x→0) sinx/x.

  4. Define left-hand limit and right-hand limit.

  5. Differentiate f(x) = x².

  6. What is the derivative of sinx?

  7. Define continuity of a function.

  8. If f(x) = 3x + 2, find f’(x).

  9. Find lim(x→1) (x² - 1)/(x - 1).

  10. What is the physical meaning of derivative?

Chapter 14: Mathematical Reasoning

  1. Define statement in logic.

  2. What is a compound statement?

  3. Define truth table.

  4. What is a tautology?

  5. Difference between converse and contrapositive.

  6. Define implication (if-then statement).

  7. What is negation of a statement?

  8. Define contradiction.

  9. What is a fallacy?

  10. Symbol for conjunction and disjunction?


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